Question

Two individuals, A and B, are finalist for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw. Outcomes of successive games are independent with P(A wins) =.3, P(B wins)= .2, P(draw)=.5. Each time a player wins a game he earns one point and opponent none, no points for draw. First player to win five points wins championship.

What is the probability that it takes just five games to obtain a champion?

First find out probability that A wins 5 games (.3x.3x.3x.3x.3=.0024)
Second find P(B wins) 5 games (.2x.2x.2x.2x.2=.00032)
Last add the probabilities of A and B (.00243+.00032=.00275)
Is this correct?
Yes, if you math is correct.

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